Abstract
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
Highlights
Quantum control has become an important topic in quantum information [1, 2], molecular chemistry [3], and atomic physics [4]
Shannon entropy in atomic calculations has further been related to various properties such as atomic ionization potential [17], molecular geometric parameters [18], chemical similarity of different functional groups [19], characteristics of correlation methods for global delocalizations [20], molecular reaction paths [21], orbital-based kinetic theory [22], highly excited states of single-particle systems [23], and nature of chemical bonds [24]
The consistency of the Shannon entropy when applied to outcomes of quantum experiments has been analyzed [25], and it is shown that Shannon entropy is fully consistent and its properties are never violated in quantum settings
Summary
Quantum control has become an important topic in quantum information [1, 2], molecular chemistry [3], and atomic physics [4]. In the recent research about quantum sliding-mode control (SMC) [26, 27], a sliding mode is defined based on the fidelity with a desired eigenstate, and the goal is to maintain the state in the mode or drive it back into the mode after measurement. Quantum von Neumann entropy is a good measure of entanglement, and it will reduce to Shannon entropy for the pure state case. It can provide a real-time noise observation and a systematic guideline to make reasonable choice of control strategy. This paper provides two primary methods to steer the discrete and continuous quantum Shannon entropy via quantum PDF control. For the discrete case, a method based on discretization approximation is provided which can directly control the entropy and achieve more accurate performance.
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